Extrapolation is dangerous because it uses a model to predict outside the range of observed data, where the existing relationship may no longer continue. The farther the prediction is from the data range, the less reliable it generally becomes.
In IB Mathematics: Analysis and Approaches, SL 4.4, a regression line models the observed linear association between two variables. For example, suppose data for study time between 1 and 6 hours produce the regression equation , where is a test score and is study time.
Using predicts , which lies within the observed range. Using predicts , but this assumes that the same linear pattern continues far beyond the available evidence. Factors such as fatigue, maximum test scores, or changes in study quality could make this prediction unrealistic.
| Method | Meaning | Reliability |
|---|---|---|
| Interpolation | Predicting within the observed range of the explanatory variable | Usually more reliable because nearby data support the model |
| Extrapolation | Predicting outside the observed range | Less reliable because the relationship may change beyond the data |
The main dangers are:
- the relationship may stop being linear;
- predictions can become impossible or unreasonable, such as a percentage above ;
- the original context or conditions may change;
- uncertainty increases as the prediction moves farther from the observed range;
- a strong correlation does not prove that one variable causes the other.
A common misconception is that a high Pearson correlation coefficient guarantees accurate predictions everywhere. It does not: measures the strength and direction of linear correlation within the observed data, not beyond it.
Exam technique: This is typically tested in an AA SL Paper 2 regression question using the command terms comment or interpret. State that the prediction is an extrapolation, identify that the input lies outside the data range, and conclude that the prediction may be unreliable because the observed trend may not continue.